The data set below has 6 values.
Find the mean absolute deviation for the data set.
If necessary, round your answer to the nearest hundredth.
4, 12, 21, 17, 6, 12
To find the mean absolute deviation for a data set, you need to follow these steps:
1. Calculate the mean. Add up all the values in the data set, and then divide the sum by the total number of values.
Let's calculate the mean:
Mean = (4 + 12 + 21 + 17 + 6 + 12) / 6 = 72 / 6 = 12
2. Find the absolute deviation for each value. Subtract the mean from each value, and take the absolute value of the difference.
Absolute Deviation for the first value (4): |4 - 12| = 8
Absolute Deviation for the second value (12): |12 - 12| = 0
Absolute Deviation for the third value (21): |21 - 12| = 9
Absolute Deviation for the fourth value (17): |17 - 12| = 5
Absolute Deviation for the fifth value (6): |6 - 12| = 6
Absolute Deviation for the sixth value (12): |12 - 12| = 0
3. Calculate the average of the absolute deviations. Add up all the absolute deviations and divide the sum by the total number of values.
Average Absolute Deviation = (8 + 0 + 9 + 5 + 6 + 0) / 6 = 28 / 6 ≈ 4.67
Therefore, the mean absolute deviation for the given data set is approximately 4.67 (rounded to the nearest hundredth).
first step: what is the mean? (sum of values)/6
now use your deviation formula.